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Asymptotic properties on high-dimensional multivariate regression M-estimation

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  • Ding, Hao
  • Qin, Shanshan
  • Wu, Yuehua
  • Wu, Yaohua

Abstract

In this paper, we work on a general multivariate regression model under the regime that both p, the number of covariates, and n, the number of observations, are large with p∕n→κ(0<κ<∞). Unlike previous works that focus on a sparse regression vector β, we consider a more interesting situation in which β is composed of two groups: components in group I are large while components in group II are small but possibly not zeros. This study aims to explore the asymptotic behavior of the ridge-regularized high-dimensional multivariate M-estimator of β in group II. By applying the double leave-one-out method, we successfully derive a nonlinear system comprised of two deterministic equations, which characterizes the risk behavior of the M-estimator. The system solution also enables us to yield asymptotic normality for each component of the M-estimator. Moreover, we present rigorous proofs to these approximations that play a critical role in deriving the system. Finally, we perform experimental validations to demonstrate the performance of the proposed system.

Suggested Citation

  • Ding, Hao & Qin, Shanshan & Wu, Yuehua & Wu, Yaohua, 2021. "Asymptotic properties on high-dimensional multivariate regression M-estimation," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:jmvana:v:183:y:2021:i:c:s0047259x21000087
    DOI: 10.1016/j.jmva.2021.104730
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    References listed on IDEAS

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    1. Bai, Z. D. & Wu, Y., 1994. "Limiting Behavior of M-Estimators of Regression Coefficients in High Dimensional Linear Models I. Scale Dependent Case," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 211-239, November.
    2. Couillet, Romain & Pascal, Frédéric & Silverstein, Jack W., 2015. "The random matrix regime of Maronna’s M-estimator with elliptically distributed samples," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 56-78.
    3. He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April.
    4. Chenlei Leng & Cheng Yong Tang, 2012. "Sparse Matrix Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1187-1200, September.
    5. Baiqi Miao & Yuehua Wu & Donghai Liu & Qian Tong, 2007. "Asymptotic Normality of the Recursive M-estimators of the Scale Parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 367-384, June.
    6. Xiaotong Shen & Wei Pan & Yunzhang Zhu, 2012. "Likelihood-Based Selection and Sharp Parameter Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 223-232, March.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    8. Shurong Zheng & Dandan Jiang & Zhidong Bai & Xuming He, 2014. "Inference on multiple correlation coefficients with moderately high dimensional data," Biometrika, Biometrika Trust, vol. 101(3), pages 748-754.
    9. Perrot-Dockès, Marie & Lévy-Leduc, Céline & Sansonnet, Laure & Chiquet, Julien, 2018. "Variable selection in multivariate linear models with high-dimensional covariance matrix estimation," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 78-97.
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